1. Field of the Invention
This invention relates generally to communication systems, and, more particularly, to wireless communication systems.
2. Description of the Related Art
Base stations in wireless communication systems provide wireless connectivity to users within a geographic area, or cell, associated with the base station. The wireless communication links between the base station and each of the users typically includes one or more downlink (or forward) channels for transmitting information from the base station to the mobile unit and one or more uplink (or reverse) channels for transmitting information from the mobile unit to the base station.
Downlink channels may be used to multicast a common radio message to several user terminals on a multicast channel. For example, users may subscribe to a multicast service that is provided by a server in a wireless communication system. The subscribers may receive the multicast information at a predetermined time or when the information becomes available. Exemplary multicast applications include the transmission of television signals, radio, audio, and/or video streaming, stock valuations, news summaries, and the like. Although multicasting information is advantageous because it permits information to be transmitted to multiple users over a single channel, the coding rate for the multicast information is typically limited by the subscriber having the lowest channel quality. For example, multicast systems are designed so that the multicast channel can be decoded by users in a large percentage of the locations served by each base station. Consequently, multicast messages transmitted by the base station must be encoded at a low rate so that even the most distant subscribers can decode the multicast transmission.
If the transmitters and/or receivers are equipped with multiple antennas, beamforming techniques can potentially be used to improve the performance of the multicasting system. For example, let nT denote the number of transmit antennas at a base station and let K indicate the number of users connected to the base station. Each user is equipped with nR receive antennas. The channel coefficients between each transmit antenna and each receive antenna at user k can be assembled into an nR×nT matrix Hk, k−1, . . . , K. The relationship between transmit and receive signals can be represented as:yk=Hkx+nk where x is an nT-dimensional vector containing the transmit signals, yk is the nR-dimensional vector of received signals at user k and nk is an nR-dimensional noise vector with a covariance of Σk=E[nknk+]. The beamforming operation that generates x is defined as x=ws, where s is a multicast signal with power P=E[|s|2] and w represents the beamforming vector whose entries indicate the complex weights applied to each transmit antenna. In order to preserve the overall signal power, the beamforming weights must satisfy the requirement ∥w∥=1. In a wide band system such as a system that uses orthogonal frequency division multiplexing, the matrices and vectors described above may be functions of frequency and therefore the above equations would describe what happens on any specific narrow subband of the wide band system.
The beamforming weights can be adjusted using information available at the transmitter. For example, statistical channel state information can be used to adjust the beamforming weights to influence the average signal-to-interference-and-noise ratios (SINR) at the receivers. The problem of determining optimal beamforming weights based on the SINR can be defined using the average SINR for the kth user: SINRk(w)=Pw+Θkw where Θk the covariance matrix:Θk=E[Hk+Σk−1Hk]where the expectation is defined over the fading within Hk. In the illustrated case, the channel statistics are not a function of frequency and so the beamforming weights are also independent of frequency. The optimum beamforming vector is defined by the set of beamforming weights that maximize the minimum data rate offered within the coverage area. Thus, the problem of finding the optimum beamforming vector may be expressed as:
  w  =      arg    ⁢                  ⁢                  max                                          w                                -          1                    ⁢              min        ⁢                                  ⁢                              SINR            _                    k                ⁢                                  ⁢                  (          w          )                    where the minimization is taken over all users within the appropriate coverage area. However, finding an optimal beamforming solution in a MIMO wireless communication system using the approach described above is an NP-hard problem.